# Licensed under a 3-clause BSD style license - see LICENSE.rst
import logging
import numpy as np
from astropy.coordinates import Angle, SkyOffsetFrame
from astropy.table import Table
from gammapy.data import FixedPointingInfo
from gammapy.irf import EDispMap, FoVAlignment, PSFMap
from gammapy.maps import Map, RegionNDMap
from gammapy.modeling.models import PowerLawSpectralModel
from gammapy.stats import WStatCountsStatistic
from gammapy.utils.coordinates import sky_to_fov
from gammapy.utils.regions import compound_region_to_regions
__all__ = [
"make_counts_rad_max",
"make_edisp_kernel_map",
"make_edisp_map",
"make_map_background_irf",
"make_map_exposure_true_energy",
"make_psf_map",
"make_theta_squared_table",
]
log = logging.getLogger(__name__)
[docs]def make_map_exposure_true_energy(
pointing, livetime, aeff, geom, use_region_center=True
):
"""Compute exposure map.
This map has a true energy axis, the exposure is not combined
with energy dispersion.
Parameters
----------
pointing : `~astropy.coordinates.SkyCoord`
Pointing direction
livetime : `~astropy.units.Quantity`
Livetime
aeff : `~gammapy.irf.EffectiveAreaTable2D`
Effective area
geom : `~gammapy.maps.WcsGeom`
Map geometry (must have an energy axis)
use_region_center: bool
If geom is a RegionGeom, whether to just
consider the values at the region center
or the instead the average over the whole region
Returns
-------
map : `~gammapy.maps.WcsNDMap`
Exposure map
"""
if not use_region_center:
coords, weights = geom.get_wcs_coord_and_weights()
else:
coords, weights = geom.get_coord(sparse=True), None
offset = coords.skycoord.separation(pointing)
exposure = aeff.evaluate(offset=offset, energy_true=coords["energy_true"])
data = (exposure * livetime).to("m2 s")
meta = {"livetime": livetime, "is_pointlike": aeff.is_pointlike}
if not use_region_center:
data = np.average(data, axis=1, weights=weights)
return Map.from_geom(geom=geom, data=data.value, unit=data.unit, meta=meta)
def _map_spectrum_weight(map, spectrum=None):
"""Weight a map with a spectrum.
This requires map to have an "energy" axis.
The weights are normalised so that they sum to 1.
The mean and unit of the output image is the same as of the input cube.
At the moment this is used to get a weighted exposure image.
Parameters
----------
map : `~gammapy.maps.Map`
Input map with an "energy" axis.
spectrum : `~gammapy.modeling.models.SpectralModel`
Spectral model to compute the weights.
Default is power-law with spectral index of 2.
Returns
-------
map_weighted : `~gammapy.maps.Map`
Weighted image
"""
if spectrum is None:
spectrum = PowerLawSpectralModel(index=2.0)
# Compute weights vector
energy_edges = map.geom.axes["energy_true"].edges
weights = spectrum.integral(
energy_min=energy_edges[:-1], energy_max=energy_edges[1:]
)
weights /= weights.sum()
shape = np.ones(len(map.geom.data_shape))
shape[0] = -1
return map * weights.reshape(shape.astype(int))
[docs]def make_map_background_irf(
pointing, ontime, bkg, geom, oversampling=None, use_region_center=True
):
"""Compute background map from background IRFs.
Parameters
----------
pointing : `~gammapy.data.FixedPointingInfo` or `~astropy.coordinates.SkyCoord`
Observation pointing
- If a `~gammapy.data.FixedPointingInfo` is passed, FOV coordinates are properly computed.
- If a `~astropy.coordinates.SkyCoord` is passed, FOV frame rotation is not taken into account.
ontime : `~astropy.units.Quantity`
Observation ontime. i.e. not corrected for deadtime
see https://gamma-astro-data-formats.readthedocs.io/en/latest/irfs/full_enclosure/bkg/index.html#notes)
bkg : `~gammapy.irf.Background3D`
Background rate model
geom : `~gammapy.maps.WcsGeom`
Reference geometry
oversampling: int
Oversampling factor in energy, used for the background model evaluation.
use_region_center: bool
If geom is a RegionGeom, whether to just
consider the values at the region center
or the instead the sum over the whole region
Returns
-------
background : `~gammapy.maps.WcsNDMap`
Background predicted counts sky cube in reco energy
"""
# TODO:
# This implementation can be improved in two ways:
# 1. Create equal time intervals between TSTART and TSTOP and sum up the
# background IRF for each interval. This is instead of multiplying by
# the total ontime. This then handles the rotation of the FoV.
# 2. Use the pointing table (does not currently exist in CTA files) to
# obtain the RA DEC and time for each interval. This then considers that
# the pointing might change slightly over the observation duration
# Get altaz coords for map
if oversampling is not None:
geom = geom.upsample(factor=oversampling, axis_name="energy")
coords = {"energy": geom.axes["energy"].edges.reshape((-1, 1, 1))}
pointing_radec = (
pointing.radec if isinstance(pointing, FixedPointingInfo) else pointing
)
if not use_region_center:
image_geom = geom.to_wcs_geom().to_image()
region_coord, weights = geom.get_wcs_coord_and_weights()
idx = image_geom.coord_to_idx(region_coord)
sky_coord = region_coord.skycoord
d_omega = image_geom.solid_angle().T[idx]
else:
image_geom = geom.to_image()
map_coord = image_geom.get_coord()
sky_coord = map_coord.skycoord
d_omega = image_geom.solid_angle()
if bkg.has_offset_axis:
coords["offset"] = sky_coord.separation(pointing_radec)
else:
if bkg.fov_alignment == FoVAlignment.ALTAZ:
if not isinstance(pointing, FixedPointingInfo):
raise (
TypeError,
"make_map_background_irf requires FixedPointingInfo if BackgroundIRF.fov_alignement is ALTAZ",
)
altaz_coord = sky_coord.transform_to(pointing.altaz_frame)
# Compute FOV coordinates of map relative to pointing
fov_lon, fov_lat = sky_to_fov(
altaz_coord.az, altaz_coord.alt, pointing.altaz.az, pointing.altaz.alt
)
elif bkg.fov_alignment == FoVAlignment.RADEC:
# Create OffsetFrame
frame = SkyOffsetFrame(origin=pointing_radec)
pseudo_fov_coord = sky_coord.transform_to(frame)
fov_lon = pseudo_fov_coord.lon
fov_lat = pseudo_fov_coord.lat
else:
raise ValueError(
f"Unsupported background coordinate system: {bkg.fov_alignment!r}"
)
coords["fov_lon"] = fov_lon
coords["fov_lat"] = fov_lat
bkg_de = bkg.integrate_log_log(**coords, axis_name="energy")
data = (bkg_de * d_omega * ontime).to_value("")
if not use_region_center:
data = np.sum(weights * data, axis=2)
bkg_map = Map.from_geom(geom, data=data)
if oversampling is not None:
bkg_map = bkg_map.downsample(factor=oversampling, axis_name="energy")
return bkg_map
[docs]def make_psf_map(psf, pointing, geom, exposure_map=None):
"""Make a psf map for a single observation
Expected axes : rad and true energy in this specific order
The name of the rad MapAxis is expected to be 'rad'
Parameters
----------
psf : `~gammapy.irf.PSF3D`
the PSF IRF
pointing : `~astropy.coordinates.SkyCoord`
the pointing direction
geom : `~gammapy.maps.Geom`
the map geom to be used. It provides the target geometry.
rad and true energy axes should be given in this specific order.
exposure_map : `~gammapy.maps.Map`, optional
the associated exposure map.
default is None
Returns
-------
psfmap : `~gammapy.irf.PSFMap`
the resulting PSF map
"""
coords = geom.get_coord(sparse=True)
# Compute separations with pointing position
offset = coords.skycoord.separation(pointing)
# Compute PSF values
data = psf.evaluate(
energy_true=coords["energy_true"],
offset=offset,
rad=coords["rad"],
)
# Create Map and fill relevant entries
psf_map = Map.from_geom(geom, data=data.value, unit=data.unit)
psf_map.normalize(axis_name="rad")
return PSFMap(psf_map, exposure_map)
[docs]def make_edisp_map(edisp, pointing, geom, exposure_map=None, use_region_center=True):
"""Make a edisp map for a single observation
Expected axes : migra and true energy in this specific order
The name of the migra MapAxis is expected to be 'migra'
Parameters
----------
edisp : `~gammapy.irf.EnergyDispersion2D`
the 2D Energy Dispersion IRF
pointing : `~astropy.coordinates.SkyCoord`
the pointing direction
geom : `~gammapy.maps.Geom`
the map geom to be used. It provides the target geometry.
migra and true energy axes should be given in this specific order.
exposure_map : `~gammapy.maps.Map`, optional
the associated exposure map.
default is None
use_region_center: Bool
If geom is a RegionGeom, whether to just
consider the values at the region center
or the instead the average over the whole region
Returns
-------
edispmap : `~gammapy.irf.EDispMap`
the resulting EDisp map
"""
# Compute separations with pointing position
if not use_region_center:
coords, weights = geom.get_wcs_coord_and_weights()
else:
coords, weights = geom.get_coord(sparse=True), None
offset = coords.skycoord.separation(pointing)
# Compute EDisp values
data = edisp.evaluate(
offset=offset,
energy_true=coords["energy_true"],
migra=coords["migra"],
)
if not use_region_center:
data = np.average(data, axis=2, weights=weights)
# Create Map and fill relevant entries
edisp_map = Map.from_geom(geom, data=data.to_value(""), unit="")
edisp_map.normalize(axis_name="migra")
return EDispMap(edisp_map, exposure_map)
[docs]def make_edisp_kernel_map(
edisp, pointing, geom, exposure_map=None, use_region_center=True
):
"""Make a edisp kernel map for a single observation
Expected axes : (reco) energy and true energy in this specific order
The name of the reco energy MapAxis is expected to be 'energy'.
The name of the true energy MapAxis is expected to be 'energy_true'.
Parameters
----------
edisp : `~gammapy.irf.EnergyDispersion2D`
the 2D Energy Dispersion IRF
pointing : `~astropy.coordinates.SkyCoord`
the pointing direction
geom : `~gammapy.maps.Geom`
the map geom to be used. It provides the target geometry.
energy and true energy axes should be given in this specific order.
exposure_map : `~gammapy.maps.Map`, optional
the associated exposure map.
default is None
use_region_center: Bool
If geom is a RegionGeom, whether to just
consider the values at the region center
or the instead the average over the whole region
Returns
-------
edispmap : `~gammapy.irf.EDispKernelMap`
the resulting EDispKernel map
"""
# Use EnergyDispersion2D migra axis.
migra_axis = edisp.axes["migra"]
# Create temporary EDispMap Geom
new_geom = geom.to_image().to_cube([migra_axis, geom.axes["energy_true"]])
edisp_map = make_edisp_map(
edisp, pointing, new_geom, exposure_map, use_region_center
)
return edisp_map.to_edisp_kernel_map(geom.axes["energy"])
[docs]def make_theta_squared_table(
observations, theta_squared_axis, position, position_off=None
):
"""Make theta squared distribution in the same FoV for a list of `Observation`
objects.
The ON theta2 profile is computed from a given distribution, on_position.
By default, the OFF theta2 profile is extracted from a mirror position
radially symmetric in the FOV to pos_on.
The ON and OFF regions are assumed to be of the same size, so the normalisation
factor between both region alpha = 1.
Parameters
----------
observations: `~gammapy.data.Observations`
List of observations
theta_squared_axis : `~gammapy.maps.geom.MapAxis`
Axis of edges of the theta2 bin used to compute the distribution
position : `~astropy.coordinates.SkyCoord`
Position from which the on theta^2 distribution is computed
position_off : `astropy.coordinates.SkyCoord`
Position from which the OFF theta^2 distribution is computed.
Default: reflected position w.r.t. to the pointing position
Returns
-------
table : `~astropy.table.Table`
Table containing the on counts, the off counts, acceptance, off acceptance and alpha
for each theta squared bin.
"""
if not theta_squared_axis.edges.unit.is_equivalent("deg2"):
raise ValueError("The theta2 axis should be equivalent to deg2")
table = Table()
table["theta2_min"] = theta_squared_axis.edges[:-1]
table["theta2_max"] = theta_squared_axis.edges[1:]
table["counts"] = 0
table["counts_off"] = 0
table["acceptance"] = 0.0
table["acceptance_off"] = 0.0
alpha_tot = np.zeros(len(table))
livetime_tot = 0
create_off = position_off is None
for observation in observations:
separation = position.separation(observation.events.radec)
counts, _ = np.histogram(separation**2, theta_squared_axis.edges)
table["counts"] += counts
if create_off:
# Estimate the position of the mirror position
pos_angle = observation.pointing_radec.position_angle(position)
sep_angle = observation.pointing_radec.separation(position)
position_off = observation.pointing_radec.directional_offset_by(
pos_angle + Angle(np.pi, "rad"), sep_angle
)
# Angular distance of the events from the mirror position
separation_off = position_off.separation(observation.events.radec)
# Extract the ON and OFF theta2 distribution from the two positions.
counts_off, _ = np.histogram(separation_off**2, theta_squared_axis.edges)
table["counts_off"] += counts_off
# Normalisation between ON and OFF is one
acceptance = np.ones(theta_squared_axis.nbin)
acceptance_off = np.ones(theta_squared_axis.nbin)
table["acceptance"] += acceptance
table["acceptance_off"] += acceptance_off
alpha = acceptance / acceptance_off
alpha_tot += alpha * observation.observation_live_time_duration.to_value("s")
livetime_tot += observation.observation_live_time_duration.to_value("s")
alpha_tot /= livetime_tot
table["alpha"] = alpha_tot
stat = WStatCountsStatistic(table["counts"], table["counts_off"], table["alpha"])
table["excess"] = stat.n_sig
table["sqrt_ts"] = stat.sqrt_ts
table["excess_errn"] = stat.compute_errn()
table["excess_errp"] = stat.compute_errp()
table.meta["ON_RA"] = position.icrs.ra
table.meta["ON_DEC"] = position.icrs.dec
return table
[docs]def make_counts_rad_max(geom, rad_max, events):
"""Extract the counts using for the ON region size the values in the
`RAD_MAX_2D` table.
Parameters
----------
geom : `~gammapy.maps.RegionGeom`
reference map geom
rad_max : `~gammapy.irf.RadMax2D`
the RAD_MAX_2D table IRF
events : `~gammapy.data.EventList`
event list to be used to compute the ON counts
Returns
-------
counts : `~gammapy.maps.RegionNDMap`
Counts vs estimated energy extracted from the ON region.
"""
selected_events = events.select_rad_max(
rad_max=rad_max, position=geom.region.center
)
counts = Map.from_geom(geom=geom)
counts.fill_events(selected_events)
return counts
def make_counts_off_rad_max(geom_off, rad_max, events):
"""Extract the OFF counts from a list of point regions and given rad max.
This methods does **not** check for overlap of the regions defined by rad_max.
Parameters
----------
geom_off: `~gammapy.maps.RegionGeom`
reference map geom for the on region
rad_max: `~gammapy.irf.RadMax2D`
the RAD_MAX_2D table IRF
events: `~gammapy.data.EventList`
event list to be used to compute the OFF counts
Returns
-------
counts_off : `~gammapy.maps.RegionNDMap`
OFF Counts vs estimated energy extracted from the ON region.
"""
if not geom_off.is_all_point_sky_regions:
raise ValueError(
f"Only supports PointSkyRegions, got {geom_off.region} instead"
)
counts_off = RegionNDMap.from_geom(geom=geom_off)
for off_region in compound_region_to_regions(geom_off.region):
selected_events = events.select_rad_max(
rad_max=rad_max, position=off_region.center
)
counts_off.fill_events(selected_events)
return counts_off